Problem: User ainta decided to paint a wall. The wall consists of n2 tiles, that are arranged in an n × n table. Some tiles are painted, and the others are not. As he wants to paint it beautifully, he will follow the rules below.

  1. Firstly user ainta looks at the wall. If there is at least one painted cell on each row and at least one painted cell on each column, he stops coloring. Otherwise, he goes to step 2. 
  2. User ainta choose any tile on the wall with uniform probability. 
  3. If the tile he has chosen is not painted, he paints the tile. Otherwise, he ignores it. 
  4. Then he takes a rest for one minute even if he doesn't paint the tile. And then ainta goes to step 1. 



However ainta is worried if it would take too much time to finish this work. So he wants to calculate the expected time needed to paint the wall by the method above. Help him find the expected time. You can assume that choosing and painting any tile consumes no time at all. 

Input

The first line contains two integers n and m (1 ≤ n ≤ 2·103; 0 ≤ m ≤ min(n2, 2·104)) — the size of the wall and the number of painted cells.

Next m lines goes, each contains two integers ri and ci (1 ≤ ri, ci ≤ n) — the position of the painted cell. It is guaranteed that the positions are all distinct. Consider the rows of the table are numbered from 1 to n. Consider the columns of the table are numbered from 1 to n.

Output

In a single line print the expected time to paint the wall in minutes. Your answer will be considered correct if it has at most 10 - 4 absolute or relative error.

Examples

Input

5 2
2 3
4 1


Output

11.7669491886


Input

2 2
1 1
1 2


Output

2.0000000000


Input

1 1
1 1


Output

0.0000000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:36777216")
using namespace std;
template <class T>
inline T &RD(T &);
template <class T>
inline void OT(const T &);
inline long long RD() {
  long long x;
  return RD(x);
}
inline double &RF(double &);
inline double RF() {
  double x;
  return RF(x);
}
inline char *RS(char *s);
inline char &RC(char &c);
inline char RC();
inline char &RC(char &c) {
  scanf(" %c", &c);
  return c;
}
inline char RC() {
  char c;
  return RC(c);
}
template <class T>
inline T &RDD(T &);
inline long long RDD() {
  long long x;
  return RDD(x);
}
template <class T0, class T1>
inline T0 &RD(T0 &x0, T1 &x1) {
  RD(x0), RD(x1);
  return x0;
}
template <class T0, class T1, class T2>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2) {
  RD(x0), RD(x1), RD(x2);
  return x0;
}
template <class T0, class T1, class T2, class T3>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  RD(x0), RD(x1), RD(x2), RD(x3);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);
  return x0;
}
template <class T0, class T1>
inline void OT(const T0 &x0, const T1 &x1) {
  OT(x0), OT(x1);
}
template <class T0, class T1, class T2>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2) {
  OT(x0), OT(x1), OT(x2);
}
template <class T0, class T1, class T2, class T3>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3) {
  OT(x0), OT(x1), OT(x2), OT(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5, const T6 &x6) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);
}
inline char &RC(char &a, char &b) {
  RC(a), RC(b);
  return a;
}
inline char &RC(char &a, char &b, char &c) {
  RC(a), RC(b), RC(c);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d) {
  RC(a), RC(b), RC(c), RC(d);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e) {
  RC(a), RC(b), RC(c), RC(d), RC(e);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g);
  return a;
}
inline double &RF(double &a, double &b) {
  RF(a), RF(b);
  return a;
}
inline double &RF(double &a, double &b, double &c) {
  RF(a), RF(b), RF(c);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d) {
  RF(a), RF(b), RF(c), RF(d);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e) {
  RF(a), RF(b), RF(c), RF(d), RF(e);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f, double &g) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g);
  return a;
}
inline void RS(char *s1, char *s2) { RS(s1), RS(s2); }
inline void RS(char *s1, char *s2, char *s3) { RS(s1), RS(s2), RS(s3); }
template <class T0, class T1>
inline void RDD(T0 &a, T1 &b) {
  RDD(a), RDD(b);
}
template <class T0, class T1, class T2>
inline void RDD(T0 &a, T1 &b, T2 &c) {
  RDD(a), RDD(b), RDD(c);
}
template <class T>
inline void RST(T &A) {
  memset(A, 0, sizeof(A));
}
template <class T>
inline void FLC(T &A, int x) {
  memset(A, x, sizeof(A));
}
template <class T>
inline void CLR(T &A) {
  A.clear();
}
template <class T0, class T1>
inline void RST(T0 &A0, T1 &A1) {
  RST(A0), RST(A1);
}
template <class T0, class T1, class T2>
inline void RST(T0 &A0, T1 &A1, T2 &A2) {
  RST(A0), RST(A1), RST(A2);
}
template <class T0, class T1, class T2, class T3>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  RST(A0), RST(A1), RST(A2), RST(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);
}
template <class T0, class T1>
inline void FLC(T0 &A0, T1 &A1, int x) {
  FLC(A0, x), FLC(A1, x);
}
template <class T0, class T1, class T2>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x);
}
template <class T0, class T1, class T2, class T3>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x),
      FLC(A6, x);
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, less<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(priority_queue<T, vector<T>, greater<T> > &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(stack<T> &S) {
  while (!S.empty()) S.pop();
}
template <class T0, class T1>
inline void CLR(T0 &A0, T1 &A1) {
  CLR(A0), CLR(A1);
}
template <class T0, class T1, class T2>
inline void CLR(T0 &A0, T1 &A1, T2 &A2) {
  CLR(A0), CLR(A1), CLR(A2);
}
template <class T0, class T1, class T2, class T3>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);
}
template <class T>
inline void CLR(T &A, int n) {
  for (int i = 0; i < n; ++i) CLR(A[i]);
}
template <class T>
inline bool EPT(T &a) {
  return a.empty();
}
template <class T>
inline T &SRT(T &A) {
  sort(A.begin(), A.end());
  return A;
}
template <class T, class C>
inline T &SRT(T &A, C B) {
  sort(A.begin(), A.end(), B);
  return A;
}
template <class T>
inline T &RVS(T &A) {
  reverse(A.begin(), A.end());
  return A;
}
template <class T>
inline T &UNQQ(T &A) {
  A.resize(unique(A.begin(), A.end()) - A.begin());
  return A;
}
template <class T>
inline T &UNQ(T &A) {
  SRT(A);
  return UNQQ(A);
}
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const long long INFF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-9;
const double OO = 1e20;
const double PI = acos(-1.0);
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};
template <class T>
inline T &checkMin(T &a, const T b) {
  if (b < a) a = b;
  return a;
}
template <class T>
inline T &checkMax(T &a, const T b) {
  if (a < b) a = b;
  return a;
}
template <class T>
inline T &checkMin(T &a, T &b, const T x) {
  checkMin(a, x), checkMin(b, x);
  return a;
}
template <class T>
inline T &checkMax(T &a, T &b, const T x) {
  checkMax(a, x), checkMax(b, x);
  return a;
}
template <class T, class C>
inline T &checkMin(T &a, const T b, C c) {
  if (c(b, a)) a = b;
  return a;
}
template <class T, class C>
inline T &checkMax(T &a, const T b, C c) {
  if (c(a, b)) a = b;
  return a;
}
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline T min(T a, T b, T c, T d, T e) {
  return min(min(min(a, b), min(c, d)), e);
}
template <class T>
inline T max(T a, T b, T c, T d, T e) {
  return max(max(max(a, b), max(c, d)), e);
}
template <class T>
inline T sqr(T a) {
  return a * a;
}
template <class T>
inline T cub(T a) {
  return a * a * a;
}
template <class T>
inline T ceil(T x, T y) {
  return (x - 1) / y + 1;
}
template <class T>
T abs(T x) {
  return x > 0 ? x : -x;
}
inline int sgn(double x) { return x < -EPS ? -1 : x > EPS; }
inline int sgn(double x, double y) { return sgn(x - y); }
inline double cos(double a, double b, double c) {
  return (sqr(a) + sqr(b) - sqr(c)) / (2 * a * b);
}
inline double cot(double x) { return 1. / tan(x); };
inline double sec(double x) { return 1. / cos(x); };
inline double csc(double x) { return 1. / sin(x); };
namespace BO {
inline bool _1(int x, int i) { return bool(x & 1 << i); }
inline bool _1(long long x, int i) { return bool(x & 1LL << i); }
inline long long _1(int i) { return 1LL << i; }
inline long long _U(int i) { return _1(i) - 1; };
inline int reverse_bits(int x) {
  x = ((x >> 1) & 0x55555555) | ((x << 1) & 0xaaaaaaaa);
  x = ((x >> 2) & 0x33333333) | ((x << 2) & 0xcccccccc);
  x = ((x >> 4) & 0x0f0f0f0f) | ((x << 4) & 0xf0f0f0f0);
  x = ((x >> 8) & 0x00ff00ff) | ((x << 8) & 0xff00ff00);
  x = ((x >> 16) & 0x0000ffff) | ((x << 16) & 0xffff0000);
  return x;
}
inline long long reverse_bits(long long x) {
  x = ((x >> 1) & 0x5555555555555555LL) | ((x << 1) & 0xaaaaaaaaaaaaaaaaLL);
  x = ((x >> 2) & 0x3333333333333333LL) | ((x << 2) & 0xccccccccccccccccLL);
  x = ((x >> 4) & 0x0f0f0f0f0f0f0f0fLL) | ((x << 4) & 0xf0f0f0f0f0f0f0f0LL);
  x = ((x >> 8) & 0x00ff00ff00ff00ffLL) | ((x << 8) & 0xff00ff00ff00ff00LL);
  x = ((x >> 16) & 0x0000ffff0000ffffLL) | ((x << 16) & 0xffff0000ffff0000LL);
  x = ((x >> 32) & 0x00000000ffffffffLL) | ((x << 32) & 0xffffffff00000000LL);
  return x;
}
template <class T>
inline bool odd(T x) {
  return x & 1;
}
template <class T>
inline bool even(T x) {
  return !odd(x);
}
template <class T>
inline T low_bit(T x) {
  return x & -x;
}
template <class T>
inline T high_bit(T x) {
  T p = low_bit(x);
  while (p != x) x -= p, p = low_bit(x);
  return p;
}
template <class T>
inline T cover_bit(T x) {
  T p = 1;
  while (p < x) p <<= 1;
  return p;
}
template <class T>
inline int cover_idx(T x) {
  int p = 0;
  while (_1(p) < x) ++p;
  return p;
}
inline int clz(int x) { return __builtin_clz(x); }
inline int clz(long long x) { return __builtin_clzll(x); }
inline int ctz(int x) { return __builtin_ctz(x); }
inline int ctz(long long x) { return __builtin_ctzll(x); }
inline int lg2(int x) { return !x ? -1 : 31 - clz(x); }
inline int lg2(long long x) { return !x ? -1 : 63 - clz(x); }
inline int low_idx(int x) { return !x ? -1 : ctz(x); }
inline int low_idx(long long x) { return !x ? -1 : ctz(x); }
inline int high_idx(int x) { return lg2(x); }
inline int high_idx(long long x) { return lg2(x); }
inline int parity(int x) { return __builtin_parity(x); }
inline int parity(long long x) { return __builtin_parityll(x); }
inline int count_bits(int x) { return __builtin_popcount(x); }
inline int count_bits(long long x) { return __builtin_popcountll(x); }
}  // namespace BO
using namespace BO;
namespace CG {
inline double dist2(double x, double y) { return sqr(x) + sqr(y); }
struct Po {
  double x, y;
  Po(double x = 0, double y = 0) : x(x), y(y) {}
  void in() { RF(x, y); }
  void out() { printf("(%.2f,%.2f)", x, y); }
  inline friend istream &operator>>(istream &i, Po &p) {
    return i >> p.x >> p.y;
  }
  inline friend ostream &operator<<(ostream &o, Po p) {
    return o << "(" << p.x << ", " << p.y << ")";
  }
  Po operator-() const { return Po(-x, -y); }
  Po &operator+=(const Po &p) {
    x += p.x, y += p.y;
    return *this;
  }
  Po &operator-=(const Po &p) {
    x -= p.x, y -= p.y;
    return *this;
  }
  Po &operator*=(double k) {
    x *= k, y *= k;
    return *this;
  }
  Po &operator/=(double k) {
    x /= k, y /= k;
    return *this;
  }
  Po &operator*=(const Po &p) { return *this = *this * p; }
  Po &operator/=(const Po &p) { return *this = *this / p; }
  Po operator+(const Po &p) const { return Po(x + p.x, y + p.y); }
  Po operator-(const Po &p) const { return Po(x - p.x, y - p.y); }
  Po operator*(double k) const { return Po(x * k, y * k); }
  Po operator/(double k) const { return Po(x / k, y / k); }
  Po operator*(const Po &p) const {
    return Po(x * p.x - y * p.y, y * p.x + x * p.y);
  }
  Po operator/(const Po &p) const {
    return Po(x * p.x + y * p.y, y * p.x - x * p.y) / p.len2();
  }
  bool operator==(const Po &p) const { return !sgn(x, p.x) && !sgn(y, p.y); };
  bool operator!=(const Po &p) const { return sgn(x, p.x) || sgn(y, p.y); }
  bool operator<(const Po &p) const {
    return sgn(x, p.x) < 0 || !sgn(x, p.x) && sgn(y, p.y) < 0;
  }
  bool operator<=(const Po &p) const {
    return sgn(x, p.x) < 0 || !sgn(x, p.x) && sgn(y, p.y) <= 0;
  }
  bool operator>(const Po &p) const { return !(*this <= p); }
  bool operator>=(const Po &p) const { return !(*this < p); }
  double len2() const { return dist2(x, y); }
  double len() const { return sqrt(len2()); }
  double arg() const { return atan2(y, x); }
  Po &_1() { return *this /= len(); }
  Po &conj() {
    y = -y;
    return *this;
  }
  Po &lt() {
    swap(x, y), x = -x;
    return *this;
  }
  Po &rt() {
    swap(x, y), y = -y;
    return *this;
  }
  Po &rot(double a, const Po &o = Po()) {
    *this -= o;
    *this *= Po(cos(a), sin(a));
    return *this += o;
  }
};
inline double dot(double x1, double y1, double x2, double y2) {
  return x1 * x2 + y1 * y2;
}
inline double dot(const Po &a, const Po &b) { return dot(a.x, a.y, b.x, b.y); }
inline double dot(const Po &p0, const Po &p1, const Po &p2) {
  return dot(p1 - p0, p2 - p0);
}
inline double det(double x1, double y1, double x2, double y2) {
  return x1 * y2 - x2 * y1;
}
inline double det(const Po &a, const Po &b) { return det(a.x, a.y, b.x, b.y); }
inline double det(const Po &p0, const Po &p1, const Po &p2) {
  return det(p1 - p0, p2 - p0);
}
inline double ang(const Po &p0, const Po &p1) {
  return acos(dot(p0, p1) / p0.len() / p1.len());
}
inline double ang(const Po &p0, const Po &p1, const Po &p2) {
  return ang(p1 - p0, p2 - p0);
}
inline double ang(const Po &p0, const Po &p1, const Po &p2, const Po &p3) {
  return ang(p1 - p0, p3 - p2);
}
inline double dist2(const Po &a, const Po &b) {
  return dist2(a.x - b.x, a.y - b.y);
}
template <class T1, class T2>
inline int dett(const T1 &x, const T2 &y) {
  return sgn(det(x, y));
}
template <class T1, class T2, class T3>
inline int dett(const T1 &x, const T2 &y, const T3 &z) {
  return sgn(det(x, y, z));
}
template <class T1, class T2, class T3, class T4>
inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  return sgn(det(x, y, z, w));
}
template <class T1, class T2>
inline int dott(const T1 &x, const T2 &y) {
  return sgn(dot(x, y));
}
template <class T1, class T2, class T3>
inline int dott(const T1 &x, const T2 &y, const T3 &z) {
  return sgn(dot(x, y, z));
}
template <class T1, class T2, class T3, class T4>
inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  return sgn(dot(x, y, z, w));
}
template <class T1, class T2>
inline double arg(const T1 &x, const T2 &y) {
  double a = ang(x, y);
  return ~dett(x, y) ? a : 2 * PI - a;
}
template <class T1, class T2, class T3>
inline double arg(const T1 &x, const T2 &y, const T3 &z) {
  double a = ang(x, y, z);
  return ~dett(x, y, z) ? a : 2 * PI - a;
}
template <class T1, class T2, class T3, class T4>
inline double arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  double a = ang(x, y, z, w);
  return ~dett(x, y, z, w) ? a : 2 * PI - a;
}
template <class T1, class T2>
inline double dist(const T1 &x, const T2 &y) {
  return sqrt(dist2(x, y));
}
template <class T1, class T2, class T3>
inline double dist(const T1 &x, const T2 &y, const T3 &z) {
  return sqrt(dist2(x, y, z));
}
inline Po _1(Po p) { return p._1(); }
inline Po conj(Po p) { return p.conj(); }
inline Po lt(Po p) { return p.lt(); }
inline Po rt(Po p) { return p.rt(); }
inline Po rot(Po p, double a, const Po &o = Po()) { return p.rot(a, o); }
inline Po operator*(double k, const Po &p) { return p * k; }
inline Po operator/(double k, const Po &p) { return conj(p) * k / p.len2(); }
struct Line {
  Po a, b;
  Line(const Po &a = Po(), const Po &b = Po()) : a(a), b(b) {}
  Line(double x0, double y0, double x1, double y1)
      : a(Po(x0, y0)), b(Po(x1, y1)) {}
  Line(const Line &l) : a(l.a), b(l.b) {}
  Line(double A, double B, double C) {
    C = -C;
    if (!::sgn(A))
      a = Po(0, C / B), b = Po(1, C / B);
    else if (!::sgn(B))
      a = Po(C / A, 0), b = Po(C / A, 1);
    else
      a = Po(0, C / B), b = Po(1, (C - A) / B);
  }
  void in() { a.in(), b.in(); }
  inline friend istream &operator>>(istream &i, Line &p) {
    return i >> p.a >> p.b;
  }
  inline friend ostream &operator<<(ostream &o, Line p) {
    return o << p.a << "-" << p.b;
  }
  Line operator+(const Po &x) const { return Line(a + x, b + x); }
  Line operator-(const Po &x) const { return Line(a - x, b - x); }
  Line operator*(double k) const { return Line(a * k, b * k); }
  Line operator/(double k) const { return Line(a / k, b / k); }
  Po operator*(const Line &) const;
  Po d() const { return b - a; }
  double len2() const { return d().len2(); }
  double len() const { return d().len(); }
  double arg() const { return d().arg(); }
  int sgn(const Po &p) const { return dett(a, b, p); }
  int sgn(const Line &) const;
  bool sameSgn(const Po &p1, const Po &p2) const { return sgn(p1) == sgn(p2); }
  void getEquation(double &K, double &B) const {
    K = ::sgn(a.x, b.x) ? (b.y - a.y) / (b.x - a.x) : OO;
    B = a.y - K * a.x;
  }
  void getEquation(double &A, double &B, double &C) const {
    A = a.y - b.y, B = b.x - a.x, C = det(a, b);
  }
  Line &push(double r) {
    Po v = d()._1().lt() * r;
    a += v, b += v;
    return *this;
  }
};
inline double dot(const Line &l1, const Line &l2) {
  return dot(l1.d(), l2.d());
}
inline double dot(const Line &l, const Po &p) { return dot(l.a, l.b, p); }
inline double dot(const Po &p, const Line &l) { return dot(p, l.a, l.b); }
inline double det(const Line &l1, const Line &l2) {
  return det(l1.d(), l2.d());
}
inline double det(const Line &l, const Po &p) { return det(l.a, l.b, p); }
inline double det(const Po &p, const Line &l) { return det(p, l.a, l.b); }
inline double ang(const Line &l0, const Line &l1) {
  return ang(l0.d(), l1.d());
}
inline double ang(const Line &l, const Po &p) { return ang(l.a, l.b, p); }
inline double ang(const Po &p, const Line &l) { return ang(p, l.a, l.b); }
inline int Line::sgn(const Line &l) const { return dett(*this, l); }
inline Po Line::operator*(const Line &l) const {
  return a + d() * det(a, l) / det(*this, l);
}
inline Po operator&(const Po &p, const Line &l) {
  return l * Line(p, p + l.d().lt());
}
inline Po operator%(const Po &p, const Line &l) { return p & l * 2 - p; }
inline Line push(Line l, double r) { return l.push(r); }
struct Seg : public Line {
  Seg(const Po &a = Po(), const Po &b = Po()) : Line(a, b) {}
  Seg(double x0, double y0, double x1, double y1) : Line(x0, y0, x1, y1) {}
  Seg(const Line &l) : Line(l) {}
  Seg(const Po &a, double alpha) : Line(a, alpha) {}
  Seg(double A, double B, double C) : Line(A, B, C) {}
  inline int sgn(const Po &p) const;
  inline int sgn(const Line &l) const;
  inline bool qrt(const Seg &l) const;
  inline int sgn(const Seg &l) const;
};
inline int Seg::sgn(const Po &p) const { return -dott(p, a, b); }
inline int Seg::sgn(const Line &l) const { return sgn(*this * l); }
inline bool Seg::qrt(const Seg &l) const {
  return min(a.x, b.x) <= max(l.a.x, l.b.x) &&
         min(l.a.x, l.b.x) <= max(a.x, b.x) &&
         min(a.y, b.y) <= max(l.a.y, l.b.y) &&
         min(l.a.y, l.b.y) <= max(a.y, b.y);
}
inline int Seg::sgn(const Seg &l) const {
  if (!qrt(l)) return -1;
  int d1 = dett(a, b, l.a), d2 = dett(a, b, l.b), d3 = dett(l.a, l.b, a),
      d4 = dett(l.a, l.b, b);
  if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 1;
  return ((!d1 && dott(l.a - a, l.a - b) <= 0) ||
          (!d2 && dott(l.b - a, l.b - b) <= 0) ||
          (!d3 && dott(a - l.a, a - l.b) <= 0) ||
          (!d4 && dott(b - l.a, b - l.b) <= 0))
             ? 0
             : -1;
}
inline double dist2(const Line &l, const Po &p) {
  return sqr(fabs(det(l.d(), p - l.a))) / l.len2();
}
inline double dist2(const Line &l1, const Line &l2) {
  return dett(l1, l2) ? 0 : dist2(l1, l2.a);
}
inline double dist2(const Seg &l, const Po &p) {
  Po pa = p - l.a, pb = p - l.b;
  if (dott(l.d(), pa) <= 0) return pa.len2();
  if (dott(l.d(), pb) >= 0) return pb.len2();
  return dist2(Line(l), p);
}
inline double dist2(const Seg &s, const Line &l) {
  Po v1 = s.a - l.a, v2 = s.b - l.a;
  double d1 = det(l.d(), v1), d2 = det(l.d(), v2);
  return sgn(d1) != sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2))) / l.len2();
}
inline double dist2(const Seg &l1, const Seg &l2) {
  if (~l1.sgn(l2))
    return 0;
  else
    return min(dist2(l2, l1.a), dist2(l2, l1.b), dist2(l1, l2.a),
               dist2(l1, l2.b));
}
template <class T1, class T2>
inline double dist2(const T1 &a, const T2 &b) {
  return dist2(b, a);
}
}  // namespace CG
using namespace CG;
template <class T>
inline T &RD(T &x) {
  char c;
  while (!isdigit((c = getchar())))
    ;
  x = c - '0';
  while (isdigit((c = getchar()))) x = x * 10 + c - '0';
  return x;
}
template <class T>
inline T &RDD(T &x) {
  char c;
  while ((c = getchar()), c != '-' && !isdigit(c))
    ;
  if (c == '-') {
    x = '0' - (c = getchar());
    while (isdigit((c = getchar()))) x = x * 10 + '0' - c;
  } else {
    x = c - '0';
    while (isdigit((c = getchar()))) x = x * 10 + c - '0';
  }
  return x;
}
inline double &RF(double &x) {
  char c;
  while ((c = getchar()), c != '-' && c != '.' && !isdigit(c))
    ;
  if (c == '-')
    if ((c = getchar()) == '.') {
      x = 0;
      double l = 1;
      while (isdigit((c = getchar()))) l /= 10, x = x * 10 + '0' - c;
      x *= l;
    } else {
      x = '0' - c;
      while (isdigit((c = getchar()))) x = x * 10 + '0' - c;
      if (c == '.') {
        double l = 1;
        while (isdigit((c = getchar()))) l /= 10, x = x * 10 + '0' - c;
        x *= l;
      }
    }
  else if (c == '.') {
    x = 0;
    double l = 1;
    while (isdigit((c = getchar()))) l /= 10, x = x * 10 + c - '0';
    x *= l;
  } else {
    x = c - '0';
    while (isdigit((c = getchar()))) x = x * 10 + c - '0';
    if (c == '.') {
      double l = 1;
      while (isdigit((c = getchar()))) l /= 10, x = x * 10 + c - '0';
      x *= l;
    }
  }
  return x;
}
inline char *RS(char *s) {
  scanf("%s", s);
  return s;
}
long long last_ans;
int Case;
template <class T>
inline void OT(const T &x) {
  printf("%.9f\n", x);
}
const int N = 2009;
double dp[N][N];
bool row[N], col[N];
int n, r, c;
int main() {
  r = c = RD(n);
  for (int ____T = RD(); ____T--;) row[RD() - 1] = col[RD() - 1] = 1;
  for (int i = 0; i < n; ++i) r -= row[i], c -= col[i];
  for (int i = 1; i <= n; ++i)
    dp[0][i] = dp[i][0] = dp[i - 1][0] + ((double)n / i);
  for (int i = 1; i <= n; ++i)
    for (int j = 1; j <= n; ++j)
      dp[i][j] = (dp[i - 1][j - 1] * i * j + dp[i - 1][j] * i * (n - j) +
                  dp[i][j - 1] * j * (n - i) + n * n) /
                 (n * (i + j) - i * j);
  OT(dp[r][c]);
}